Question

what is the value of u?
work

Explanation:

Step1: Use the perpendicular bisector theorem

Since \( FH\) is the perpendicular bisector of \( GI\) (\( GF = FI=15\)), then \( GH = HI\) (Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment).

Step2: Set up the equation

We know that \( GH = 3u\) and \( HI=u + 14\). So, \(3u=u + 14\).

Step3: Solve the equation for \(u\)

Subtract \(u\) from both sides: \(3u-u=u + 14-u\).
We get \(2u=14\).
Divide both sides by 2: \(u=\frac{14}{2}\).

Answer:

\(7\)